When the product is synchronized to a clock from an external device, the displayed tempo fluctuates. Is this normal?

Yes, this is normal and not a problem. Chordcat uses the received clock pulses to calculate the tempo, however, the clock pulses always have a little bit of jitter (fluctuation) between each other.
These fluctuations make the displayed tempo fluctuate, but it doesn't mean the devices are going out of sync, and the fluctuations can't be detected by the human hear.